Is there a googol of anything?

21 October 2012

Question

Hi Chris, I hear there is a maths radio show this weekend so the Spriggs family has a maths question for you (it may also have some physics in it...!): A concept that we enjoy in the Spriggs household is that of the googol, i.e. 10 to the power 100 or a 1 followed by a hundred 0s. I believe that the googol may be a pretty useless concept, if there isn't a googol of anything in the universe... I said this to my boys and added that you don't need a number to describe something that doesn't exist... Since that day, when our older son was about 7,our two boys have been trying to come up with a googol of something. They started with the grains of sand in the Sahara Desert. That is a very very small number. We eventually reached the number of photons in the universe. I don't know the answer to this, but I got to 10 to the power 87. Which leaves it 10 trillion times smaller than a googol. But I have never been able to prove this. It would be good if the Naked Scientists could oblige?! And could they get us past a googol of something, anything? If nothing else, it has taught our boys the laws of indices! Best regards, Andy

Answer

Matt - A googol is a great number in that, it is a number that exists just because it has a nice name. There's nothing that we really have a googol of, but someone thought, "wouldn't a 1 with 100 zeros be a great number?" so they called it a googol. You could hear him emphasising gooGOL because it's spelled G O O G O L. The Google search engine is named after this but they spelled it differently. He's absolutely correct. If you're going to try to count objects, you won't find a googol of anything. So, even going right up to number of protons in the universe, which I think is - physicists argue between 1079 to 1081, so it's a 1 with somewhere between 79 and 81 zeros. But I have found one thing which we have more than a googol of in the universe.

Chris - Well, should we ask Ginny if she can guess what it is?

Ginny - I don't know. I mean, I was thinking about neurons because they make an awful lot of connections, but I think when we are thinking about this, it probably wouldn't be quite that many, even if you include all the animals on the Earth.

Chris - 1011 nerve cells in the brain, 1,000 connections per nerve cells per brain, so that would probably be about 1014,so we're still a long way short of Matt's googol.

Matt - Actually, you're not far off from what I decided on because when you're talking about connections, well suddenly, you're looking at different ways of combining things. And so, I looked at how many ways you can shuffle a pack of cards. So if you got a pack of 52 cards and you shuffle it, you can work out there's about 1067, It's 8 times 1067 ways to shuffle a pack of cards which is a lot more than the number of grains of sand in the Sahara. In fact, if you've got a pack of cards, with just 27 cards, you would have about 1028 different ways to shuffle them. If you want a googol, if you get a pack of cards with 70 cards - so you're going to need your normal pack and then get 18 from a pack maybe with a different colour on the front or the back so you can tell them apart - if you shuffle 70 cards, There's a googol of possible ways to arrange them.

Chris - Beautiful. I was thinking of a similar example, Matt because I was looking at the power of passwords on the internet. Someone was asking a question on our forum and they were discussing the power of encryption and saying, "if I took a brute force attempt to crack a password just by taking random choices, how many possible combinations of a password encrypted with a certain number of bits of encryption?" And you end up with something which will take trillions of centuries to solve and the number of solutions I think is way more than a googol.

Matt - Yes, and again, you're looking at number of possible combinations. So in fact, a password is pretty close to a pack of cards because you've got the alphabet, upper and lower case and then you do actually get extra symbols, and bits and pieces. So, if you've got a password of even just 8 characters, you're already up in the very high tens of thousands and much bigger than that, you're into millions, billions and well off very quickly.

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